Question

Which is a zero of the quadratic function f(x) = 16x2 32x − 9?

Answer 1

A zero of a function is the value of x for which f(x) = 0
f(x) = 16x^2 + 32x - 9 = 0
16x^2 - 4x + 36x - 9 = 0
(16x^2 - 4x) + (36x - 9) = 0
4x(4x - 1) + 9(4x - 1) = 0
(4x + 9)(4x - 1) = 0
4x + 9 = 0 and 4x - 1 = 0
4x = -9 and 4x = 1
x = -9/4 and x = 1/4

Answer 2

Solution:

The given Quadratic function whose zero we have to find is:

  $16 x^2 - 32 x -9=0\\\\16x^2-36 x + 4 x -9=0\\\\4 x\times (4 x -9)+1 \times(4 x -9)=0\\\\(4 x +1)(4 x-9)=0\\\\4 x +1=0 \text{or} ,4 x -9=0\\\\ x=\frac{-1}{4} \text{or} , x=\frac{9}{4}$

So,

     $x=\frac{-1}{4} \text{or} , x=\frac{9}{4}$, are zero of Quadratic function.

If the equation was like this

$\rightarrow 16 x^2 + 32 x -9=0\\\\16 x^2+36 x -4 x -9=0\\\\4 x\times (4 x +9)-1 \times(4 x +9)=0\\\\(4 x -1)(4 x+9)=0\\\\4 x -1=0 \text{or} ,4 x +9=0\\\\ x=\frac{1}{4} \text{or} , x=\frac{-9}{4}$

So,

     $x=\frac{1}{4} \text{or} , x=\frac{-9}{4}$, are zero of Quadratic function.